FBX with Weight or Deformation support?
The only animated mesh deformations Blender can export to FBX are:


Armature-driven ones.
Relative shape keys.


So if you can bake your physics into shapekeys, or use a 'fake-physics' armature, it should work.

PS: don’t know Max, but I would bet their “deformations” are similar to Blender’s “shape keys”?